Advances in adaptive stabilization, command following, and disturbance rejection

Three fundamental objectives in feedback control are stabilization, command following, and disturbance rejection, while many feedback control problems can be framed as combinations of stabilization, command following, and disturbance rejection. This dissertation presents advances in all three adaptive control problems. More specifically, this dissertation presents new adaptive control methods that operate under relaxed model assumptions or relaxed assumptions on the exogenous command and disturbance signals. Two primary areas of research are presented in this dissertation, namely, parameter-monotonic adaptive control and discrete-time adaptive control.; Parameter-monotonic adaptive control for continuous-time systems uses a simple adaptive law to increase a scalar parameter until a control objective such as stabilization, command following, or disturbance rejection has been achieved. The first primary result is parameter-monotonic adaptive stabilization for nonlinear time-varying systems with full-state feedback and matched uncertainty. Next, parameter-monotonic adaptive controllers are presented for stabilization, command following, and disturbance rejection for minimum-phase linear systems with unknown-but-bounded relative degree.; Strictly proper discrete-time systems are never stable under high-gain feedback. Consequently, parameter-monotonic adaptive laws are ill-suited to discrete-time, and thus alternate adaptive methods must be considered. In this dissertation, a discrete-time adaptive controller is designed using windows of input and output data. The main result is an adaptive controller for stabilization, command following, and disturbance rejection for multi-input multi-output discrete-time systems with unknown exogenous dynamics.